MOSCOW – The Russian opposition has called on the authorities to annul election results marred by alleged violations and threatened more anti-Kremlin rallies as tens of thousands demonstrated across the country.

Officially, police estimates put the crowd on Moscow's Bolotnaya Square on December 10 at 20,000, although organizers cited much higher figures of up to 100,000. The event went off without significant incident and police say no one was detained.

Many media outlets said it marked the largest protest since the collapse of the Soviet Union.

In a resolution laid before demonstrators in Moscow, the opposition also demanded the release of opposition leaders Aleksei Navalny and Ilya Yashin and others who were jailed in protests this week.

"The first [demand] is the release of political prisoners who were jailed after the so-called elections and the second is new elections," Yevgenia Chirikova, an environmentalist and key opposition leader, told RFE/RL after the Moscow demonstration. "Of course, having new elections is one of our definite demands, but there are rather a lot of conditions."

The chairman of Russia's Central Election Commission, Vladimir Churov

Those conditions include a call for the resignation of Central Election Commission Chairman Vladimir Churov and an investigation into his work, as well as an investigation into vote-fraud allegations and changes to the law on registering political parties to allow all opposition parties to participate in future elections.

The organizers say they will protest again on December 24 if the government has not acceded to their demands.

'New Era In Civil Society'

Amid roars of "Russia without Putin!" and "New elections!" demonstrators at the protest heralded what they called a "new era in civil society."

One rally participant, who gave her name as Lidia and identified herself as a 29-year-old civil engineer, told RFE/RL that she came to protest the "fraudulent, falsified election." She said the large-scale protests were "an historic event."

"We have never seen so many people out on the street, standing united against barefaced, shameless lies," she said.

The anti-Kremlin rallies sweeping through Russia are seen as the biggest challenge yet to Prime Minister Vladimir Putin's authority and underscore simmering public discontent as he prepares to run in a presidential election scheduled for March 2012.

Putin is widely expected to win, but analysts say he has never been on the back foot like this before.

A statement released by Putin's press secretary, Dmitry Peskov, acknowledged the day's protests by people "displeased" with the elections but noted demonstrations in support of the elections in recent days.

WATCH: Footage of the Moscow rallies by RFE/RL's Russian Service (contains interviews with protesters in Russian)

A deputy chairman of the Central Election Commission told Interfax that the results of the election have been confirmed and there are no grounds for reviewing them.

The ruling United Russia party won just under 50 percent at the December 4 State Duma polls, down from 64 percent in 2007.

The opposition insists that the ruling party's real results were much lower. Monitors from the Organization for Security and Cooperation in Europe (OSCE) said the election was tilted in favor of United Russia.

"The New Times" editor Yevgenia Albats

Speaking from a podium at the rally, Yevgenia Albats, editor of the independent "The New Times," urged the crowd to keep up its demands and to collect "tens of millions of signatures" for the "resignation of Putin and [President Dmitry] Medvedev."

Churov, the Central Election Commission head, said earlier this week that dozens of online videos purporting to capture electoral fraud at polling stations were faked.

He claimed the videos had been filmed in makeshift apartment studios and that the allegations of fraud were "lies."

Similar demonstrations were held in dozens of cities from St. Petersburg in the West to Vladivostok in the Far East and Arkhangelsk in the Arctic north. Most passed peacefully, although some were dispersed by riot police. Interfax reported that 130 were arrested in total across the country.

Sparse State Media Coverage

Aleksandr Bobkov participated in the demonstration in Vladivostok and expressed his frustration with the ruling party.

"Everyone is sick of living under a regime that prevents its citizens from expressing their will freely," he said, suggesting that Russians were being forced "to choose from the rotten ingredients of the soup and bankrupt politicians."

"And I am talking not just about United Russia but also about the opposition," he added.

Oleg, a 35-year-old IT engineer who attended the protest in Moscow, told RFE/RL that he is particularly disturbed by the state media's failure to cover the demonstrations of the last few days.

"We would like these events to be given objective coverage on television, because rallies have been taking place for a few days now and central television is reporting absolutely nothing," he said.

State media ignored two major opposition protests in Moscow earlier this week that saw more than 1,000 people arrested, but all the main networks provided some sparse coverage of the protests on December 10.

A Diverse Crowd

The protests drew a diverse crowd. Demonstrators in Moscow waved flags for nationalists, communists, liberals, and sexual minorities as snow fell on the square next to the Moscow River, with temperatures hovering around 0 degrees Celsius.

Organizers emphasized their "common goals," although divisions in the crowd occasionally surfaced. After a speech from a right-wing opposition leader, a cluster of nationalists began chanting “Revolution! Revolution!” and were met with boos and jeers from others.

Aleksei Navalny was jailed for his part in earlier antigovernment protests.

The authorities have appeared increasingly nervous at this week's rallies, which saw celebrity blogger and de facto opposition leader Aleksei Navalny and Ilya Yashin, a leading figure in the Solidarity movement, jailed for 15 days for "disobeying police instructions."

Thousands of Interior Ministry troops were deployed in the capital earlier this week, and tentative attempts have been made to try and discourage would-be protesters.

On December 9, authorities in Moscow announced that high school students would be required to attend school on the day of the demonstrations. And chief health inspector Gennady Onishchenko warned Russians not to attend demonstrations in order to avoid spreading the flu.

Counterdemonstrations

Pro-Kremlin youth groups look certain to respond to the protests with their own demonstrations.

The Interfax news agency quoted Timur Prokopenko, head of the youth wing of the ruling United Russia party, as saying his organization is prepared to organize a demonstration of up to 170,000 people in support of the official results of the December 4 elections.

Prokopenko added that the country cannot be bound by the opinions of "minorities and politically marginalized people who act with the support of the West."

Chirikova maintained that the opposition would continue to ride the momentum of this week's demonstrations.

"We will have more protests," she said. "We are looking forward to the release of our comrades. I am sure when they come out we will have more events."